ANSWER
(C) d=1
EXPLANATION
The given equation is
[tex] \frac{ - 3d}{ {d}^{2} - 2d - 8} + \frac{3}{d - 4} = \frac{ - 2}{d + 2} [/tex]
Factor the first fraction to get,
[tex] \frac{ - 3d}{(d + 2)(d - 4)} + \frac{3}{d - 4} = \frac{ - 2}{d + 2} [/tex]
Multiply through by (d+2)(d-4)
[tex] - 3d + 3(d + 2) = - 2(d - 4)[/tex]
Expand:
[tex] - 3d + 3d + 6 = - 2d + 8[/tex]
[tex] 6 = - 2d + 8[/tex]
[tex]6 - 8= - 2d[/tex]
[tex] - 2 = - 2d[/tex]
divide both sides by -2
[tex]d = 1[/tex]
